THE HISTORY AND SHAPE OF THE TEST-PIECE. 329 the first factor to the second is not great, and the change in total percentage with each linear increment is not marked. If the length were zero, the percentage of elongation would be infinite, while, if the length were infinite, the percentage of extension would be represented by the permanent set of those portions of the bar where no necking occurs. The true curve expressing the law of relative elongation is undoubtedly an hyperbola, one asymptote of which will correspond to a length of zero, while the other will be the percentage due to the permanent set, which will vary with every kind of steel. TABLE XVI-P. Influence upon the Elongation of Changes in the Length.* No. of bar. Dimensions; inches. Ratio of length to diameter. Elongation; per cent. Length. Diameter. 1 LOT 0.077 2.91 42.0 2 8.94 0.677 5.81 82.0 8 5.91 0.677 8.72 29.3 4 7.8T 0.677 11.60 27.2 6 9.84 0.677 14.50 26.6 0 11.81 0.677 17.40 26.0 7 18.78 0.677 20.30 25.1 8 15.75 0.677 28.80 25.0 0 17.72 0.677 26.20 24.9 The elongation in the portion of the piece which does not undergo "necking" may be calculated from Table XVI-0. As a matter of experience, a length of about two inches includes the region wherein necking occurs, and this length is a constant, no matter what the total length of the test-piece may be. A test-piece two inches long is practically all "neck," while in one four inches long there will be one length of two inches which is all neck, and two inches which will remain nearly a true cylinder after fracture. In the case of the 2-inch test-pieces, given,in Table XVI-0, the average elongation was 47.43 per cent., representing a linear elongation of 0.9486 inches. In the case of the 4-inch test-pieces the stretch, by the above assumption, was the same in the necked region, while the total elongation was 36.11 per cent., representing a linear elongation of 1.4444 inches. Hence, the elongation in the two inches of the cylindrical portion was 1.4444—0.9486=0.4958 inches, or 24.79 per cent. * Barba, Prbc. French Soc. Civil Eng., Vol. 1,1880, p. 682.